A new material is being tested for possible use in the brake shoes of automobiles. These shoes are expected to last for at least 75,000 miles. Fifteen sets of four of these experimental shoes are subjected to accelerated life testing. The random variable X, the number of shoes in each group of four that fail early, is assumed to be binomially distributed with n = 4 and p unknown. Find the maximum likelihood estimate for p based on these data:
1 0 1 0 2 1 0 1
0 1 0 0 0 1 0
If an early failure rate in excess of 10% is unacceptable from a business point of view, would you have some doubts concerning the use of this new material?